6.1.2 The Poisson’s adiabat The thermodynamical potential of a system consisting of N molecules of ideal gas at temperature T and pressure P can be written as [12]: The entropy of this system Φ = const · N + NT lnP − Nc P T lnT. (6.10) S = const · N − NlnP + Nc P lnT. (6.11) As at adiabatic process, the entropy remains constant −NT lnP + Nc P T lnT = const, (6.12) we can write the equation for relation of averaged pressure in a system with its volume (The Poisson’s adiabat) [12]: ̂P V ˜γ = const, (6.13) where ˜γ = c P cV is the exponent of adiabatic constant. In considered case taking into account of Eqs.(6.6) and (6.5), we obtain As V 1/3 ∼ R 0, we have for equilibrium condition ˜γ = cP c V = 1 3 . (6.14) ̂P R 0 = const. (6.15) 6.2 The mass-radius ratio Using Eq.(6.1) from Eq.(6.15), we use the equation for dependence of masses of stars on their radii: M 2 = const (6.16) R 3 0 This equation shows the existence of internal constraint of chemical parameters of equilibrium state of a star. Indeed, the substitution of obtained determinations Eq.(5.37) and (5.38)) into Eq.(6.16) gives: Z ∼ (A/Z) 5/6 (6.17) Simultaneously the observational data of masses, of radii and their temperatures was obtained by astronomers for close binary stars [11]. The dependence of radii of these stars over these masses is shown in Fig.6.1 on double logarithmic scale. The solid line shows the result of fitting of measurement data R 0 ∼ M 0.68 . It is close to theoretical dependence R 0 ∼ M 2/3 (Eq.6.16) which is shown by dotted line. 41